The desire to supplicate such a dua is a sign of your immense love for reciting the Qur'an. The English translation of the dua you have mentioned is:

"Oh Allah, grant me the honour of reciting the Holy Qur'an in my grave after I die."

This world is Darul-'Amal (the Abode of Action). As such, only those virtuous deeds acquired in one's lifetime are credited to one's Book of Deeds. In the Hereafter, which is Darul-Jaza' (the Abode of Recompense), a person will only be rewarded for such actions carried out during one's lifespan. For this reason, a person should recite the Qur'an abundantly until death overtakes him/her, and this is actual achievement.

As for your query, it would be permissible for you to make such a dua (supplication), since such a dua does not fall under the category of Mustahalat (impossibilities). Numerous incidents have been narrated showing the possibility of an inhabitant of the grave reciting the Qur'an. Although these narrations are of such a nature that they are not fit for evidence independently, they collectively serve as a proof of the common factor found in them, viz. the possibility of an inhabitant of the grave reciting the Qur'an.

Imam al-Suyuti mentions a few incidents in his book: 'Bushra-al-Kaib-bi-Liqai-al-Habib'. Hereunder, we quote one of these accounts:

Ibn Abbas (Radi-Allahu-'anhu) narrates that a Sah?bi sat on a grave (the narration of al-Tirmidhi mention: 'pitched his tent on a grave') not knowing that it was a grave. Suddenly (he heard) a person inside the grave reciting Surah al-Mulk, until he (i.e. the inhabitant of the grave) completed it (i.e. Surah al-Mulk). So, this person came to Nabi (Sallallahu Alaihi Wa Sallam) and informed him (about this experience). Nabi (Sallall?hu Alaihi Wa Sallam) said, "It (i.e. Surah al-Mulk) is the protector and it is the saviour from the punishment of the grave.) (p. 45, Daru Ya'rab)

We hereby make this dua as well: "Oh Allah, give us the Taufeeq (Divine Guidance) to recite the Qur'an abundantly in this world, and give us the honour of reciting it in the grave too." Amin.